What does the question mean by "path"? Does it mean the arc length, or the normal deviation, or the tangential deviation?Noiro said:Homework Statement
Steel ruler tip's oscillation amplitude is 1cm, frequency 5Hz. What is the path the ruler's tip goes within 2 seconds?
Homework Equations
I think I need to find a period so the equations would be T=1/5 s but I'm not sure.
The Attempt at a Solution
I don't know how to solve it so I would be grateful if someone could help me.
Hootenanny said:What does the question mean by "path"? Does it mean the arc length, or the normal deviation, or the tangential deviation?
Oke doke.Noiro said:It is the arc length
Hootenanny said:Oke doke.
As you correctly say, the period of oscillations is 1/5 seconds. What else do you think we need to work out in order to solve this problem?
What do you usually need to work out the arc length (two things)?Noiro said:Maybe a phase of an oscillation? I'm not sure though. What do we need?
Hootenanny said:What do you usually need to work out the arc length (two things)?
Noiro said:Measure of a central angle and radius?
Correct. So, what is the radius?Noiro said:Measure of a central angle and radius?
No it isn't, the amplitude is given, but that isn't the arc length.RoyalCat said:but the arc length is given
Erm... yes you can.RoyalCat said:and you can't calculate it using the central angle and radius as those are unknowns for this problem.
Hootenanny said:Correct. So, what is the radius?
You have to work it out...Noiro said:I don't know. What is it?
Hootenanny said:You have to work it out...
HINT: If you weren't given the frequency, but were instead given the radius of the pendulum, what equation would you use to determine the period of the oscillations?
That is correct.Noiro said:I think it's T=2pi sqrt(L/g)
Hootenanny said:That is correct.
Just one minor point, do you have a diagram associated with this question? I'm assuming that this steel rule is hanging vertically and is oscillating in plane like a pendulum. Would that be correct?
Ahh I see. I had originally envisaged a pendulum-like set up. However, this case actually turns out to be a lot simpler than the case that I had originally envisaged. The steel rule is acting like a mass-spring system and in this case to a fairly high degree of accuracy the tip of the rule doesn't trace an arc. Instead, it traces [approximately] a straight line.Noiro said:No it's embedded in a clamp. I hope you can imagine what it looks like.
Hootenanny said:Ahh I see. I had originally envisaged a pendulum-like set up. However, this case actually turns out to be a lot simpler than the case that I had originally envisaged. The steel rule is acting like a mass-spring system and in this case to a fairly high degree of accuracy the tip of the rule doesn't trace an arc. Instead, it traces [approximately] a straight line.
So, let's forget about determining the radius. Instead, can you tell me how far the tip of the rule travels in one complete oscillation?
As RoyalCat has said, 1cm is the maximal displacement (i.e. the distance between its equilibrium position and one of the turning points). What is a full oscillation in terms of turning points and the equilibrium position?Noiro said:Well if amplitude is 1cm then I guess it's 2cm. Am I right?
Hootenanny said:As RoyalCat has said, 1cm is the maximal displacement (i.e. the distance between its equilibrium position and one of the turning points). What is a full oscillation in terms of turning points and the equilibrium position?
Correct. So, if the ruler has a period of 1/5 seconds, how many oscillations occur in 2 seconds? Hence how far does the tip of the ruler travel in 2 seconds?Noiro said:So it's 4cm right?
Hootenanny said:Correct. So, if the ruler has a period of 1/5 seconds, how many oscillations occur in 2 seconds? Hence how far does the tip of the ruler travel in 2 seconds?
Sounds good to me!Noiro said:So in 2 seconds occur 10 oscillations and tip of the ruler travels 40cm. Am I right?
Hootenanny said:Sounds good to me!
Apologies for the earlier confusion regarding the orientation of the ruler. Thanks to RoyalCat for pointing out the correct set up.
The purpose of solving oscillation problems with steel ruler measurements is to accurately measure and analyze the oscillations of objects, such as pendulums or springs, in order to understand their motion and behavior.
Steel ruler measurements provide a precise and reliable way to measure the amplitude, frequency, and period of oscillations. This data can then be used to calculate important parameters, such as the object's mass or spring constant.
Some common techniques include measuring the time for a certain number of oscillations, measuring the distance the object travels in one oscillation, and using trigonometric functions to analyze the data.
Yes, there are some potential errors and limitations. For example, the ruler may not be perfectly straight, there could be human error in recording the measurements, and external factors such as air resistance may affect the motion of the object.
Solving oscillation problems with steel ruler measurements can be applied in various fields such as engineering, physics, and even music. For example, it can help in designing stable structures, understanding the behavior of mechanical systems, and tuning musical instruments.